Higher-order accurate solution to electromagnetic scattering problems are obtained at reduced computational cost in a {it p}-variable finite volume time domain method. Spatial operators of lower, including first-order accuracy, are employed locally in substantial parts of the computational domain during the solution process. The use of computationally cheaper lower order spatial operators does not affect the overall higher-order accuracy of the solution. The order of the spatial operator at a candidate cell during numerical simulation can vary in space and time and is dynamically chosen based on an order of magnitude comparison of scattered and incident fields at the cell center. Numerical results are presented for electromagnetic scattering from perfectly conducting two-dimensional scatterers subject to transverse magnetic and transverse electric illumination.
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